9984
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 30
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 36
- Divisor Sum
- 28616
- Proper Divisor Sum (Aliquot Sum)
- 18632
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 3072
- Möbius Function
- 0
- Radical
- 78
- Omega Function (Ω)
- 10
- Little Omega Function (ω)
- 3
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- no
- Perfect Cube
- no
- Pentagonal Number
- no
- Hexagonal Number
- no
- Lucas Number
- no
- Tetrahedral Number
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 42
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- no
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- yes
- Odd
- no
Appears in sequences
- Negated coefficients of Chebyshev T polynomials: [x^n](-T(n+6, x)), n >= 0.at n=7A001794
- Theta series of {D_6}* lattice.at n=35A008425
- Expansion of e.g.f. arctan(arctan(x)*arctan(x)) (even powers only).at n=4A012459
- tanh(arctan(x)*arctan(x))=2/2!*x^2-16/4!*x^4+128/6!*x^6+9984/8!*x^8...at n=4A012463
- Droll numbers: numbers > 1 whose sum of even prime factors equals the sum of odd prime factors.at n=8A019507
- a(n) = 10^n - n^2.at n=4A024116
- Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 49.at n=31A031547
- Expansion of Product_{k>=1} (1 + 3*x^k).at n=23A032308
- Number of partitions of n with equal number of parts congruent to each of 0, 1 and 4 (mod 5).at n=57A035574
- a(0) = 0; for n>0, a(n) = maximal number of regions into which space can be divided by n spheres.at n=32A046127
- Numbers that are divisible by at least 10 primes (counted with multiplicity).at n=32A046313
- Numbers that are divisible by exactly 10 primes with multiplicity.at n=21A046314
- a(n) is the number of sets of natural numbers [a,b,c,d,e] that can be produced with the numbers [0..n] such that the values of all the distinct parenthesized expressions of a-b-c-d-e are different.at n=7A054026
- Triangle of partial row sums (prs) of triangle A055252.at n=47A055584
- Numbers k such that k^16 == 1 (mod 17^3).at n=33A056088
- Maximum value seen in the final n decimal digits of 2^j for all values of j.at n=3A060458
- Numbers k such that sigma(x) = k has exactly 10 solutions.at n=14A060666
- Smallest number k for which the set of solutions to phi(x) = k has 2n-1 entries.at n=30A071387
- Least number m such that cardinality of InvPhi(m) = prime(n).at n=17A071389
- Numbers k such that Omega(k) = Omega(k+1) + Omega(k+2) + Omega(k+3) + Omega(k+4) where Omega(k) denotes the number of prime factors of k, counting multiplicity.at n=10A078094